| 1 | !> @file lpm_splitting.f90 |
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| 2 | !------------------------------------------------------------------------------! |
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| 3 | ! This file is part of the PALM model system. |
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| 4 | ! |
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| 5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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| 6 | ! terms of the GNU General Public License as published by the Free Software |
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| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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| 8 | ! version. |
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| 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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| 17 | ! Copyright 1997-2018 Leibniz Universitaet Hannover |
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| 18 | !------------------------------------------------------------------------------! |
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| 19 | ! |
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| 20 | ! Current revisions: |
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| 21 | ! ------------------ |
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| 22 | ! |
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| 23 | ! |
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| 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: lpm_splitting.f90 2718 2018-01-02 08:49:38Z raasch $ |
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| 27 | ! Corrected "Former revisions" section |
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| 28 | ! |
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| 29 | ! |
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| 30 | ! Change in file header (GPL part) |
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| 31 | ! |
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| 32 | ! Added comments |
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| 33 | ! |
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| 34 | ! |
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| 35 | ! 2263 2017-06-08 14:59:01Z schwenkel |
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| 36 | ! Initial revision |
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| 37 | ! |
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| 38 | ! |
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| 39 | ! |
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| 40 | ! Description: |
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| 41 | ! ------------ |
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| 42 | ! This routine is a part of the Lagrangian particle model. Super droplets which |
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| 43 | ! fulfill certain criterion's (e.g. a big weighting factor and a large radius) |
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| 44 | ! can be split into several super droplets with a reduced number of |
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| 45 | ! represented particles of every super droplet. This mechanism ensures an |
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| 46 | ! improved representation of the right tail of the drop size distribution with |
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| 47 | ! a feasible amount of computational costs. The limits of particle creation |
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| 48 | ! should be chosen carefully! The idea of this algorithm is based on |
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| 49 | ! Unterstrasser and Soelch, 2014. |
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| 50 | !------------------------------------------------------------------------------! |
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| 51 | SUBROUTINE lpm_splitting |
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| 52 | |
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| 53 | |
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| 54 | USE arrays_3d, & |
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| 55 | ONLY: ql |
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| 56 | |
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| 57 | USE cloud_parameters, & |
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| 58 | ONLY: rho_l |
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| 59 | |
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| 60 | USE constants, & |
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| 61 | ONLY: pi |
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| 62 | |
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| 63 | USE cpulog, & |
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| 64 | ONLY: cpu_log, log_point_s |
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| 65 | |
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| 66 | USE indices, & |
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| 67 | ONLY: nxl, nxr, nyn, nys, nzb, nzt |
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| 68 | |
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| 69 | USE kinds |
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| 70 | |
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| 71 | USE lpm_exchange_horiz_mod, & |
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| 72 | ONLY: realloc_particles_array |
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| 73 | |
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| 74 | USE particle_attributes, & |
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| 75 | ONLY: grid_particles, iran_part, initial_weighting_factor, isf, & |
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| 76 | i_splitting_mode, max_number_particles_per_gridbox, & |
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| 77 | new_particles, n_max, number_concentration, & |
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| 78 | number_of_particles, number_particles_per_gridbox, particles, & |
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| 79 | particle_type, prt_count, radius_split, splitting, & |
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| 80 | splitting_factor, splitting_factor_max, splitting_mode, & |
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| 81 | sum_new_particles, weight_factor_split |
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| 82 | |
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| 83 | USE pegrid |
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| 84 | |
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| 85 | IMPLICIT NONE |
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| 86 | |
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| 87 | INTEGER(iwp) :: i !< |
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| 88 | INTEGER(iwp) :: j !< |
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| 89 | INTEGER(iwp) :: jpp !< |
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| 90 | INTEGER(iwp) :: k !< |
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| 91 | INTEGER(iwp) :: n !< |
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| 92 | INTEGER(iwp) :: new_particles_gb !< counter of created particles within one grid box |
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| 93 | INTEGER(iwp) :: new_size !< new particle array size |
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| 94 | INTEGER(iwp) :: np !< |
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| 95 | INTEGER(iwp) :: old_size !< old particle array size |
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| 96 | |
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| 97 | LOGICAL :: first_loop_stride = .TRUE. !< flag to calculate constants only once |
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| 98 | |
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| 99 | REAL(wp) :: diameter !< diameter of droplet |
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| 100 | REAL(wp) :: dlog !< factor for DSD calculation |
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| 101 | REAL(wp) :: factor_volume_to_mass !< pre calculate factor volume to mass |
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| 102 | REAL(wp) :: lambda !< slope parameter of gamma-distribution |
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| 103 | REAL(wp) :: lwc !< liquid water content of grid box |
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| 104 | REAL(wp) :: lwc_total !< average liquid water content of cloud |
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| 105 | REAL(wp) :: m1 !< first moment of DSD |
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| 106 | REAL(wp) :: m1_total !< average over all PEs of first moment of DSD |
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| 107 | REAL(wp) :: m2 !< second moment of DSD |
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| 108 | REAL(wp) :: m2_total !< average average over all PEs second moment of DSD |
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| 109 | REAL(wp) :: m3 !< third moment of DSD |
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| 110 | REAL(wp) :: m3_total !< average average over all PEs third moment of DSD |
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| 111 | REAL(wp) :: mu !< spectral shape parameter of gamma distribution |
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| 112 | REAL(wp) :: nrclgb !< number of cloudy grid boxes (ql >= 1.0E-5 kg/kg) |
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| 113 | REAL(wp) :: nrclgb_total !< average over all PEs of number of cloudy grid boxes |
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| 114 | REAL(wp) :: nr !< number concentration of cloud droplets |
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| 115 | REAL(wp) :: nr_total !< average over all PEs of number of cloudy grid boxes |
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| 116 | REAL(wp) :: nr0 !< intercept parameter of gamma distribution |
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| 117 | REAL(wp) :: pirho_l !< pi * rho_l / 6.0 |
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| 118 | REAL(wp) :: ql_crit = 1.0E-5_wp !< threshold lwc for cloudy grid cells |
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| 119 | !< (Siebesma et al 2003, JAS, 60) |
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| 120 | REAL(wp) :: rm !< volume averaged mean radius |
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| 121 | REAL(wp) :: rm_total !< average over all PEs of volume averaged mean radius |
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| 122 | REAL(wp) :: r_min = 1.0E-6_wp !< minimum radius of approximated spectra |
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| 123 | REAL(wp) :: r_max = 1.0E-3_wp !< maximum radius of approximated spectra |
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| 124 | REAL(wp) :: sigma_log = 1.5_wp !< standard deviation of the LOG-distribution |
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| 125 | REAL(wp) :: zeta !< Parameter for DSD calculation of Seifert |
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| 126 | |
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| 127 | REAL(wp), DIMENSION(0:n_max-1) :: an_spl !< size dependent critical weight factor |
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| 128 | REAL(wp), DIMENSION(0:n_max-1) :: r_bin_mid !< mass weighted mean radius of a bin |
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| 129 | REAL(wp), DIMENSION(0:n_max) :: r_bin !< boundaries of a radius bin |
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| 130 | |
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| 131 | TYPE(particle_type) :: tmp_particle !< temporary particle TYPE |
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| 132 | |
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| 133 | CALL cpu_log( log_point_s(80), 'lpm_splitting', 'start' ) |
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| 134 | |
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| 135 | IF ( first_loop_stride ) THEN |
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| 136 | IF ( i_splitting_mode == 2 .OR. i_splitting_mode == 3 ) THEN |
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| 137 | dlog = ( LOG10(r_max) - LOG10(r_min) ) / ( n_max - 1 ) |
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| 138 | DO i = 0, n_max-1 |
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| 139 | r_bin(i) = 10.0_wp**( LOG10(r_min) + i * dlog - 0.5_wp * dlog ) |
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| 140 | r_bin_mid(i) = 10.0_wp**( LOG10(r_min) + i * dlog ) |
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| 141 | ENDDO |
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| 142 | r_bin(n_max) = 10.0_wp**( LOG10(r_min) + n_max * dlog - 0.5_wp * dlog ) |
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| 143 | ENDIF |
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| 144 | factor_volume_to_mass = 4.0_wp / 3.0_wp * pi * rho_l |
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| 145 | pirho_l = pi * rho_l / 6.0_wp |
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| 146 | IF ( weight_factor_split == -1.0_wp ) THEN |
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| 147 | weight_factor_split = 0.1_wp * initial_weighting_factor |
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| 148 | ENDIF |
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| 149 | ENDIF |
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| 150 | |
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| 151 | new_particles = 0 |
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| 152 | |
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| 153 | IF ( i_splitting_mode == 1 ) THEN |
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| 154 | |
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| 155 | DO i = nxl, nxr |
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| 156 | DO j = nys, nyn |
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| 157 | DO k = nzb+1, nzt |
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| 158 | |
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| 159 | new_particles_gb = 0 |
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| 160 | number_of_particles = prt_count(k,j,i) |
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| 161 | IF ( number_of_particles <= 0 .OR. & |
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| 162 | ql(k,j,i) < ql_crit ) CYCLE |
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| 163 | particles => grid_particles(k,j,i)%particles(1:number_of_particles) |
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| 164 | ! |
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| 165 | !-- Start splitting operations. Each particle is checked if it |
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| 166 | !-- fulfilled the splitting criterion's. In splitting mode 'const' |
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| 167 | !-- a critical radius (radius_split) a critical weighting factor |
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| 168 | !-- (weight_factor_split) and a splitting factor (splitting_factor) |
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| 169 | !-- must be prescribed (see particles_par). Super droplets which |
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| 170 | !-- have a larger radius and larger weighting factor are split into |
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| 171 | !-- 'splitting_factor' super droplets. Therefore, the weighting |
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| 172 | !-- factor of the super droplet and all created clones is reduced |
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| 173 | !-- by the factor of 'splitting_factor'. |
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| 174 | DO n = 1, number_of_particles |
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| 175 | IF ( particles(n)%particle_mask .AND. & |
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| 176 | particles(n)%radius >= radius_split .AND. & |
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| 177 | particles(n)%weight_factor >= weight_factor_split ) & |
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| 178 | THEN |
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| 179 | ! |
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| 180 | !-- Calculate the new number of particles. |
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| 181 | new_size = prt_count(k,j,i) + splitting_factor - 1 |
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| 182 | ! |
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| 183 | !-- Cycle if maximum number of particles per grid box |
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| 184 | !-- is greater than the allowed maximum number. |
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| 185 | IF ( new_size >= max_number_particles_per_gridbox ) CYCLE |
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| 186 | ! |
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| 187 | !-- Reallocate particle array if necessary. |
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| 188 | IF ( new_size > SIZE(particles) ) THEN |
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| 189 | CALL realloc_particles_array(i,j,k,new_size) |
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| 190 | ENDIF |
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| 191 | old_size = prt_count(k,j,i) |
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| 192 | ! |
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| 193 | !-- Calculate new weighting factor. |
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| 194 | particles(n)%weight_factor = & |
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| 195 | particles(n)%weight_factor / splitting_factor |
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| 196 | tmp_particle = particles(n) |
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| 197 | ! |
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| 198 | !-- Create splitting_factor-1 new particles. |
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| 199 | DO jpp = 1, splitting_factor-1 |
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| 200 | grid_particles(k,j,i)%particles(jpp+old_size) = & |
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| 201 | tmp_particle |
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| 202 | ENDDO |
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| 203 | new_particles_gb = new_particles_gb + splitting_factor - 1 |
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| 204 | ! |
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| 205 | !-- Save the new number of super droplets for every grid box. |
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| 206 | prt_count(k,j,i) = prt_count(k,j,i) + & |
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| 207 | splitting_factor - 1 |
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| 208 | ENDIF |
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| 209 | ENDDO |
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| 210 | |
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| 211 | new_particles = new_particles + new_particles_gb |
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| 212 | sum_new_particles = sum_new_particles + new_particles_gb |
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| 213 | ENDDO |
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| 214 | ENDDO |
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| 215 | ENDDO |
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| 216 | |
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| 217 | ELSEIF ( i_splitting_mode == 2 ) THEN |
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| 218 | ! |
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| 219 | !-- Initialize summing variables. |
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| 220 | lwc = 0.0_wp |
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| 221 | lwc_total = 0.0_wp |
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| 222 | m1 = 0.0_wp |
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| 223 | m1_total = 0.0_wp |
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| 224 | m2 = 0.0_wp |
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| 225 | m2_total = 0.0_wp |
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| 226 | m3 = 0.0_wp |
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| 227 | m3_total = 0.0_wp |
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| 228 | nr = 0.0_wp |
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| 229 | nrclgb = 0.0_wp |
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| 230 | nrclgb_total = 0.0_wp |
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| 231 | nr_total = 0.0_wp |
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| 232 | rm = 0.0_wp |
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| 233 | rm_total = 0.0_wp |
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| 234 | |
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| 235 | DO i = nxl, nxr |
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| 236 | DO j = nys, nyn |
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| 237 | DO k = nzb+1, nzt |
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| 238 | number_of_particles = prt_count(k,j,i) |
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| 239 | IF ( number_of_particles <= 0 .OR. & |
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| 240 | ql(k,j,i) < ql_crit ) CYCLE |
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| 241 | particles => grid_particles(k,j,i)%particles(1:number_of_particles) |
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| 242 | nrclgb = nrclgb + 1.0_wp |
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| 243 | ! |
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| 244 | !-- Calculate moments of DSD. |
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| 245 | DO n = 1, number_of_particles |
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| 246 | IF ( particles(n)%particle_mask .AND. & |
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| 247 | particles(n)%radius >= r_min ) & |
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| 248 | THEN |
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| 249 | nr = nr + particles(n)%weight_factor |
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| 250 | rm = rm + factor_volume_to_mass * & |
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| 251 | particles(n)%radius**3 * & |
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| 252 | particles(n)%weight_factor |
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| 253 | IF ( isf == 1 ) THEN |
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| 254 | diameter = particles(n)%radius * 2.0_wp |
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| 255 | lwc = lwc + factor_volume_to_mass * & |
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| 256 | particles(n)%radius**3 * & |
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| 257 | particles(n)%weight_factor |
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| 258 | m1 = m1 + particles(n)%weight_factor * diameter |
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| 259 | m2 = m2 + particles(n)%weight_factor * diameter**2 |
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| 260 | m3 = m3 + particles(n)%weight_factor * diameter**3 |
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| 261 | ENDIF |
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| 262 | ENDIF |
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| 263 | ENDDO |
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| 264 | ENDDO |
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| 265 | ENDDO |
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| 266 | ENDDO |
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| 267 | |
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| 268 | #if defined( __parallel ) |
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| 269 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
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| 270 | CALL MPI_ALLREDUCE( nr, nr_total, 1 , & |
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| 271 | MPI_REAL, MPI_SUM, comm2d, ierr ) |
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| 272 | CALL MPI_ALLREDUCE( rm, rm_total, 1 , & |
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| 273 | MPI_REAL, MPI_SUM, comm2d, ierr ) |
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| 274 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
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| 275 | CALL MPI_ALLREDUCE( nrclgb, nrclgb_total, 1 , & |
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| 276 | MPI_REAL, MPI_SUM, comm2d, ierr ) |
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| 277 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
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| 278 | CALL MPI_ALLREDUCE( lwc, lwc_total, 1 , & |
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| 279 | MPI_REAL, MPI_SUM, comm2d, ierr ) |
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| 280 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
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| 281 | CALL MPI_ALLREDUCE( m1, m1_total, 1 , & |
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| 282 | MPI_REAL, MPI_SUM, comm2d, ierr ) |
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| 283 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
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| 284 | CALL MPI_ALLREDUCE( m2, m2_total, 1 , & |
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| 285 | MPI_REAL, MPI_SUM, comm2d, ierr ) |
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| 286 | IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr ) |
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| 287 | CALL MPI_ALLREDUCE( m3, m3_total, 1 , & |
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| 288 | MPI_REAL, MPI_SUM, comm2d, ierr ) |
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| 289 | #endif |
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| 290 | |
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| 291 | ! |
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| 292 | !-- Calculate number concentration and mean volume averaged radius. |
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| 293 | nr_total = MERGE( nr_total / nrclgb_total, & |
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| 294 | 0.0_wp, nrclgb_total > 0.0_wp & |
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| 295 | ) |
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| 296 | rm_total = MERGE( ( rm_total / & |
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| 297 | ( nr_total * factor_volume_to_mass ) & |
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| 298 | )**0.3333333_wp, 0.0_wp, nrclgb_total > 0.0_wp & |
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| 299 | ) |
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| 300 | ! |
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| 301 | !-- Check which function should be used to approximate the DSD. |
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| 302 | IF ( isf == 1 ) THEN |
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| 303 | lwc_total = MERGE( lwc_total / nrclgb_total, & |
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| 304 | 0.0_wp, nrclgb_total > 0.0_wp & |
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| 305 | ) |
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| 306 | m1_total = MERGE( m1_total / nrclgb_total, & |
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| 307 | 0.0_wp, nrclgb_total > 0.0_wp & |
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| 308 | ) |
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| 309 | m2_total = MERGE( m2_total / nrclgb_total, & |
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| 310 | 0.0_wp, nrclgb_total > 0.0_wp & |
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| 311 | ) |
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| 312 | m3_total = MERGE( m3_total / nrclgb_total, & |
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| 313 | 0.0_wp, nrclgb_total > 0.0_wp & |
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| 314 | ) |
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| 315 | zeta = m1_total * m3_total / m2_total**2 |
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| 316 | mu = MAX( ( ( 1.0_wp - zeta ) * 2.0_wp + 1.0_wp ) / & |
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| 317 | ( zeta - 1.0_wp ), 0.0_wp & |
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| 318 | ) |
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| 319 | |
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| 320 | lambda = ( pirho_l * nr_total / lwc_total * & |
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| 321 | ( mu + 3.0_wp ) * ( mu + 2.0_wp ) * ( mu + 1.0_wp ) & |
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| 322 | )**0.3333333_wp |
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| 323 | nr0 = nr_total / gamma( mu + 1.0_wp ) * lambda**( mu + 1.0_wp ) |
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| 324 | |
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| 325 | DO n = 0, n_max-1 |
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| 326 | diameter = r_bin_mid(n) * 2.0_wp |
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| 327 | an_spl(n) = nr0 * diameter**mu * EXP( -lambda * diameter ) * & |
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| 328 | ( r_bin(n+1) - r_bin(n) ) * 2.0_wp |
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| 329 | ENDDO |
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| 330 | ELSEIF ( isf == 2 ) THEN |
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| 331 | DO n = 0, n_max-1 |
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| 332 | an_spl(n) = nr_total / ( SQRT( 2.0_wp * pi ) * & |
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| 333 | LOG(sigma_log) * r_bin_mid(n) & |
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| 334 | ) * & |
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| 335 | EXP( -( LOG( r_bin_mid(n) / rm_total )**2 ) / & |
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| 336 | ( 2.0_wp * LOG(sigma_log)**2 ) & |
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| 337 | ) * & |
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| 338 | ( r_bin(n+1) - r_bin(n) ) |
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| 339 | ENDDO |
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| 340 | ELSEIF( isf == 3 ) THEN |
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| 341 | DO n = 0, n_max-1 |
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| 342 | an_spl(n) = 3.0_wp * nr_total * r_bin_mid(n)**2 / rm_total**3 * & |
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| 343 | EXP( - ( r_bin_mid(n)**3 / rm_total**3 ) ) * & |
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| 344 | ( r_bin(n+1) - r_bin(n) ) |
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| 345 | ENDDO |
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| 346 | ENDIF |
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| 347 | ! |
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| 348 | !-- Criterion to avoid super droplets with a weighting factor < 1.0. |
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| 349 | an_spl = MAX(an_spl, 1.0_wp) |
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| 350 | |
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| 351 | DO i = nxl, nxr |
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| 352 | DO j = nys, nyn |
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| 353 | DO k = nzb+1, nzt |
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| 354 | number_of_particles = prt_count(k,j,i) |
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| 355 | IF ( number_of_particles <= 0 .OR. & |
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| 356 | ql(k,j,i) < ql_crit ) CYCLE |
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| 357 | particles => grid_particles(k,j,i)%particles(1:number_of_particles) |
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| 358 | new_particles_gb = 0 |
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| 359 | ! |
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| 360 | !-- Start splitting operations. Each particle is checked if it |
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| 361 | !-- fulfilled the splitting criterion's. In splitting mode 'cl_av' |
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| 362 | !-- a critical radius (radius_split) and a splitting function must |
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| 363 | !-- be prescribed (see particles_par). The critical weighting factor |
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| 364 | !-- is calculated while approximating a 'gamma', 'log' or 'exp'- |
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| 365 | !-- drop size distribution. In this mode the DSD is calculated as |
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| 366 | !-- an average over all cloudy grid boxes. Super droplets which |
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| 367 | !-- have a larger radius and larger weighting factor are split into |
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| 368 | !-- 'splitting_factor' super droplets. In this case the splitting |
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| 369 | !-- factor is calculated of weighting factor of the super droplet |
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| 370 | !-- and the approximated number concentration for droplet of such |
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| 371 | !-- a size. Due to the splitting, the weighting factor of the |
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| 372 | !-- super droplet and all created clones is reduced by the factor |
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| 373 | !-- of 'splitting_facor'. |
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| 374 | DO n = 1, number_of_particles |
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| 375 | DO np = 0, n_max-1 |
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| 376 | IF ( r_bin(np) >= radius_split .AND. & |
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| 377 | particles(n)%particle_mask .AND. & |
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| 378 | particles(n)%radius >= r_bin(np) .AND. & |
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| 379 | particles(n)%radius < r_bin(np+1) .AND. & |
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| 380 | particles(n)%weight_factor >= an_spl(np) ) & |
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| 381 | THEN |
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| 382 | ! |
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| 383 | !-- Calculate splitting factor |
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| 384 | splitting_factor = & |
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| 385 | MIN( INT( particles(n)%weight_factor / & |
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| 386 | an_spl(np) & |
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| 387 | ), splitting_factor_max & |
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| 388 | ) |
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| 389 | IF ( splitting_factor < 2 ) CYCLE |
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| 390 | ! |
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| 391 | !-- Calculate the new number of particles. |
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| 392 | new_size = prt_count(k,j,i) + splitting_factor - 1 |
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| 393 | ! |
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| 394 | !-- Cycle if maximum number of particles per grid box |
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| 395 | !-- is greater than the allowed maximum number. |
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| 396 | IF ( new_size >= max_number_particles_per_gridbox ) & |
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| 397 | CYCLE |
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| 398 | ! |
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| 399 | !-- Reallocate particle array if necessary. |
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| 400 | IF ( new_size > SIZE(particles) ) THEN |
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| 401 | CALL realloc_particles_array(i,j,k,new_size) |
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| 402 | ENDIF |
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| 403 | old_size = prt_count(k,j,i) |
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| 404 | new_particles_gb = new_particles_gb + & |
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| 405 | splitting_factor - 1 |
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| 406 | ! |
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| 407 | !-- Calculate new weighting factor. |
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| 408 | particles(n)%weight_factor = & |
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| 409 | particles(n)%weight_factor / splitting_factor |
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| 410 | tmp_particle = particles(n) |
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| 411 | ! |
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| 412 | !-- Create splitting_factor-1 new particles. |
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| 413 | DO jpp = 1, splitting_factor-1 |
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| 414 | grid_particles(k,j,i)%particles(jpp+old_size) = & |
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| 415 | tmp_particle |
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| 416 | ENDDO |
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| 417 | ! |
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| 418 | !-- Save the new number of super droplets. |
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| 419 | prt_count(k,j,i) = prt_count(k,j,i) + & |
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| 420 | splitting_factor - 1 |
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| 421 | ENDIF |
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| 422 | ENDDO |
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| 423 | ENDDO |
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| 424 | |
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| 425 | new_particles = new_particles + new_particles_gb |
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| 426 | sum_new_particles = sum_new_particles + new_particles_gb |
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| 427 | ENDDO |
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| 428 | ENDDO |
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| 429 | ENDDO |
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| 430 | |
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| 431 | ELSEIF ( i_splitting_mode == 3 ) THEN |
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| 432 | |
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| 433 | DO i = nxl, nxr |
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| 434 | DO j = nys, nyn |
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| 435 | DO k = nzb+1, nzt |
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| 436 | |
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| 437 | ! |
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| 438 | !-- Initialize summing variables. |
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| 439 | lwc = 0.0_wp |
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| 440 | m1 = 0.0_wp |
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| 441 | m2 = 0.0_wp |
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| 442 | m3 = 0.0_wp |
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| 443 | nr = 0.0_wp |
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| 444 | rm = 0.0_wp |
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| 445 | |
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| 446 | new_particles_gb = 0 |
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| 447 | number_of_particles = prt_count(k,j,i) |
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| 448 | IF ( number_of_particles <= 0 .OR. & |
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| 449 | ql(k,j,i) < ql_crit ) CYCLE |
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| 450 | particles => grid_particles(k,j,i)%particles |
|---|
| 451 | ! |
|---|
| 452 | !-- Calculate moments of DSD. |
|---|
| 453 | DO n = 1, number_of_particles |
|---|
| 454 | IF ( particles(n)%particle_mask .AND. & |
|---|
| 455 | particles(n)%radius >= r_min ) & |
|---|
| 456 | THEN |
|---|
| 457 | nr = nr + particles(n)%weight_factor |
|---|
| 458 | rm = rm + factor_volume_to_mass * & |
|---|
| 459 | particles(n)%radius**3 * & |
|---|
| 460 | particles(n)%weight_factor |
|---|
| 461 | IF ( isf == 1 ) THEN |
|---|
| 462 | diameter = particles(n)%radius * 2.0_wp |
|---|
| 463 | lwc = lwc + factor_volume_to_mass * & |
|---|
| 464 | particles(n)%radius**3 * & |
|---|
| 465 | particles(n)%weight_factor |
|---|
| 466 | m1 = m1 + particles(n)%weight_factor * diameter |
|---|
| 467 | m2 = m2 + particles(n)%weight_factor * diameter**2 |
|---|
| 468 | m3 = m3 + particles(n)%weight_factor * diameter**3 |
|---|
| 469 | ENDIF |
|---|
| 470 | ENDIF |
|---|
| 471 | ENDDO |
|---|
| 472 | |
|---|
| 473 | IF ( nr <= 0.0 .OR. rm <= 0.0_wp ) CYCLE |
|---|
| 474 | ! |
|---|
| 475 | !-- Calculate mean volume averaged radius. |
|---|
| 476 | rm = ( rm / ( nr * factor_volume_to_mass ) )**0.3333333_wp |
|---|
| 477 | ! |
|---|
| 478 | !-- Check which function should be used to approximate the DSD. |
|---|
| 479 | IF ( isf == 1 ) THEN |
|---|
| 480 | ! |
|---|
| 481 | !-- Gamma size distribution to calculate |
|---|
| 482 | !-- critical weight_factor (e.g. Marshall + Palmer, 1948). |
|---|
| 483 | zeta = m1 * m3 / m2**2 |
|---|
| 484 | mu = MAX( ( ( 1.0_wp - zeta ) * 2.0_wp + 1.0_wp ) / & |
|---|
| 485 | ( zeta - 1.0_wp ), 0.0_wp & |
|---|
| 486 | ) |
|---|
| 487 | lambda = ( pirho_l * nr / lwc * & |
|---|
| 488 | ( mu + 3.0_wp ) * ( mu + 2.0_wp ) * & |
|---|
| 489 | ( mu + 1.0_wp ) & |
|---|
| 490 | )**0.3333333_wp |
|---|
| 491 | nr0 = ( nr / (gamma( mu + 1.0_wp ) ) ) * & |
|---|
| 492 | lambda**( mu + 1.0_wp ) |
|---|
| 493 | |
|---|
| 494 | DO n = 0, n_max-1 |
|---|
| 495 | diameter = r_bin_mid(n) * 2.0_wp |
|---|
| 496 | an_spl(n) = nr0 * diameter**mu * & |
|---|
| 497 | EXP( -lambda * diameter ) * & |
|---|
| 498 | ( r_bin(n+1) - r_bin(n) ) * 2.0_wp |
|---|
| 499 | ENDDO |
|---|
| 500 | ELSEIF ( isf == 2 ) THEN |
|---|
| 501 | ! |
|---|
| 502 | !-- Lognormal size distribution to calculate critical |
|---|
| 503 | !-- weight_factor (e.g. Levin, 1971, Bradley + Stow, 1974). |
|---|
| 504 | DO n = 0, n_max-1 |
|---|
| 505 | an_spl(n) = nr / ( SQRT( 2.0_wp * pi ) * & |
|---|
| 506 | LOG(sigma_log) * r_bin_mid(n) & |
|---|
| 507 | ) * & |
|---|
| 508 | EXP( -( LOG( r_bin_mid(n) / rm )**2 ) / & |
|---|
| 509 | ( 2.0_wp * LOG(sigma_log)**2 ) & |
|---|
| 510 | ) * & |
|---|
| 511 | ( r_bin(n+1) - r_bin(n) ) |
|---|
| 512 | ENDDO |
|---|
| 513 | ELSEIF ( isf == 3 ) THEN |
|---|
| 514 | ! |
|---|
| 515 | !-- Exponential size distribution to calculate critical |
|---|
| 516 | !-- weight_factor (e.g. Berry + Reinhardt, 1974). |
|---|
| 517 | DO n = 0, n_max-1 |
|---|
| 518 | an_spl(n) = 3.0_wp * nr * r_bin_mid(n)**2 / rm**3 * & |
|---|
| 519 | EXP( - ( r_bin_mid(n)**3 / rm**3 ) ) * & |
|---|
| 520 | ( r_bin(n+1) - r_bin(n) ) |
|---|
| 521 | ENDDO |
|---|
| 522 | ENDIF |
|---|
| 523 | |
|---|
| 524 | ! |
|---|
| 525 | !-- Criterion to avoid super droplets with a weighting factor < 1.0. |
|---|
| 526 | an_spl = MAX(an_spl, 1.0_wp) |
|---|
| 527 | ! |
|---|
| 528 | !-- Start splitting operations. Each particle is checked if it |
|---|
| 529 | !-- fulfilled the splitting criterion's. In splitting mode 'gb_av' |
|---|
| 530 | !-- a critical radius (radius_split) and a splitting function must |
|---|
| 531 | !-- be prescribed (see particles_par). The critical weighting factor |
|---|
| 532 | !-- is calculated while appoximating a 'gamma', 'log' or 'exp'- |
|---|
| 533 | !-- drop size distribution. In this mode a DSD is calculated for |
|---|
| 534 | !-- every cloudy grid box. Super droplets which have a larger |
|---|
| 535 | !-- radius and larger weighting factor are split into |
|---|
| 536 | !-- 'splitting_factor' super droplets. In this case the splitting |
|---|
| 537 | !-- factor is calculated of weighting factor of the super droplet |
|---|
| 538 | !-- and theapproximated number concentration for droplet of such |
|---|
| 539 | !-- a size. Due to the splitting, the weighting factor of the |
|---|
| 540 | !-- super droplet and all created clones is reduced by the factor |
|---|
| 541 | !-- of 'splitting_facor'. |
|---|
| 542 | DO n = 1, number_of_particles |
|---|
| 543 | DO np = 0, n_max-1 |
|---|
| 544 | IF ( r_bin(np) >= radius_split .AND. & |
|---|
| 545 | particles(n)%particle_mask .AND. & |
|---|
| 546 | particles(n)%radius >= r_bin(np) .AND. & |
|---|
| 547 | particles(n)%radius < r_bin(np+1) .AND. & |
|---|
| 548 | particles(n)%weight_factor >= an_spl(np) ) & |
|---|
| 549 | THEN |
|---|
| 550 | ! |
|---|
| 551 | !-- Calculate splitting factor. |
|---|
| 552 | splitting_factor = & |
|---|
| 553 | MIN( INT( particles(n)%weight_factor / & |
|---|
| 554 | an_spl(np) & |
|---|
| 555 | ), splitting_factor_max & |
|---|
| 556 | ) |
|---|
| 557 | IF ( splitting_factor < 2 ) CYCLE |
|---|
| 558 | |
|---|
| 559 | ! |
|---|
| 560 | !-- Calculate the new number of particles. |
|---|
| 561 | new_size = prt_count(k,j,i) + splitting_factor - 1 |
|---|
| 562 | ! |
|---|
| 563 | !-- Cycle if maximum number of particles per grid box |
|---|
| 564 | !-- is greater than the allowed maximum number. |
|---|
| 565 | IF ( new_size >= max_number_particles_per_gridbox ) & |
|---|
| 566 | CYCLE |
|---|
| 567 | ! |
|---|
| 568 | !-- Reallocate particle array if necessary. |
|---|
| 569 | IF ( new_size > SIZE(particles) ) THEN |
|---|
| 570 | CALL realloc_particles_array(i,j,k,new_size) |
|---|
| 571 | ENDIF |
|---|
| 572 | ! |
|---|
| 573 | !-- Calculate new weighting factor. |
|---|
| 574 | particles(n)%weight_factor = & |
|---|
| 575 | particles(n)%weight_factor / splitting_factor |
|---|
| 576 | tmp_particle = particles(n) |
|---|
| 577 | old_size = prt_count(k,j,i) |
|---|
| 578 | ! |
|---|
| 579 | !-- Create splitting_factor-1 new particles. |
|---|
| 580 | DO jpp = 1, splitting_factor-1 |
|---|
| 581 | grid_particles(k,j,i)%particles(jpp+old_size) = & |
|---|
| 582 | tmp_particle |
|---|
| 583 | ENDDO |
|---|
| 584 | ! |
|---|
| 585 | !-- Save the new number of droplets for every grid box. |
|---|
| 586 | prt_count(k,j,i) = prt_count(k,j,i) + & |
|---|
| 587 | splitting_factor - 1 |
|---|
| 588 | new_particles_gb = new_particles_gb + & |
|---|
| 589 | splitting_factor - 1 |
|---|
| 590 | ENDIF |
|---|
| 591 | ENDDO |
|---|
| 592 | ENDDO |
|---|
| 593 | |
|---|
| 594 | new_particles = new_particles + new_particles_gb |
|---|
| 595 | sum_new_particles = sum_new_particles + new_particles_gb |
|---|
| 596 | ENDDO |
|---|
| 597 | ENDDO |
|---|
| 598 | ENDDO |
|---|
| 599 | ENDIF |
|---|
| 600 | |
|---|
| 601 | CALL cpu_log( log_point_s(80), 'lpm_splitting', 'stop' ) |
|---|
| 602 | |
|---|
| 603 | END SUBROUTINE lpm_splitting |
|---|
| 604 | |
|---|
